We recall (see [1]}, [2]}) that the affine Kac-Moody algebra \(\widehat{sl}_{n+1} is anextension of the loop algebra \) sln+1 by two additive generators, and that
the irreducible positive energy representations of \(\widehat{sl}_{n+1} of level \) k\(are parametrized by dominant weights \) (,k)\(, where \)\( is a dominant weightof \) sln+1 of level \(k\) .
